Based on the general analysis of the grand canonical partition function in
the S-matrix framework, the calculated results on symmetry energy, free energy
and entropy of dilute warm nuclear matter are presented. At a given temperature
and density, the symmetry energy or symmetry free energy of the clusterized
nuclear matter in the S-matrix formulation deviates, particularly at low
temperature and relatively higher density, in a subtle way, from the linear
dependence on the square of the isospin asymmetry parameter
X=(ΟnββΟpβ)/(Οnβ+Οpβ), contrary to those obtained for homogeneous
nucleonic matter. The symmetry coefficients, in the conventional definition,
can then be even negative. The symmetry entropy similarly shows a very
different behavior.Comment: 8 pages, 6 figures. PRC (in press